On a Monday night in late August, Sen. Lindsey Graham was traveling with a congressional delegation in Africa when the three Republicans who are challenging him in the 2014 GOP primary joined a large and strongly conservative crowd at Rep. Jeff Duncan’s annual Faith and Freedom Barbecue. To listen to Graham’s opponents tell it, that situation — a lawmaker who is far away and out-of-touch — is emblematic of the senator’s relationship with his constituents.

“The people in South Carolina are very conservative, and he’s been working with Obama and acting as if he’s the Secretary of State, when he should be representing the people of South Carolina,” said one of the challengers, Lee Bright, a state senator from the Greenville/Spartanburg area.

“He just doesn’t represent South Carolina very well,” said challenger Richard Cash, a businessman who nearly won a House seat in 2010. “He voted for Justice Sotomayor … and then he did the same thing with Justice Kagan. We don’t like his leadership on immigration — we believe it’s another Grahamnesty. He’s not just on the wrong side of the issue, he’s a leader on the wrong side.”

“I see conservatives in Washington who stood up for the Constitution, who stood for border security, who stood against amnesty, who have stood up against reckless spending and the bailouts, who have stood against liberal Supreme Court justices — and almost always you can find Sen. Graham on the other side,” said challenger Nancy Mace, a Charleston PR executive best known for being the first woman to graduate from the Citadel.

There’s no doubt Graham is vulnerable in 2014. Immigration reform, two Supreme Court votes, a perceived closeness to Barack Obama and a flirtation with liberal initiatives like cap and trade: None of that sits well with the state party’s most loyal conservative voters.

The problem for Graham’s opponents is that he’s been vulnerable before, and won handily. In 2008, Graham had recently backed another immigration reform measure that critics called amnesty. And yet he had minimal opposition and won re-election with 58 percent of the vote.

Now Graham has a lot of money in the bank, a track record of winning, and a well-deserved reputation as a smart campaigner. Add to those strengths the fact that it appears neither Bright, Mace, nor Cash has the stature, depth, or money to mount a real statewide challenge. Of the three, some experts see Bright, who in his 2010 near-victory rated highly with evangelicals, homeschoolers, and some Tea Partiers, as the most serious threat. But not a really serious threat.

Despite all those problems, there’s still real hope for Graham’s opponents. One new factor is conservative hero Jim DeMint’s decision to leave his Senate seat to head the Heritage Foundation.

“I think the standard of Jim DeMint has whetted (Republican voters’) appetite to have a senator who is more what they want,” says David Woodard, a Clemson University political scientist who runs the respected Palmetto Poll. “Tim Scott (DeMint’s replacement) is fine, but he hasn’t been there long enough. Lindsey has been there 20 years, and people are starting to think he’s never going to change.”

At the barbecue, a crowd of about 900 paid $35 each for dinner and a chance to hear Duncan and the evening’s big guest, 2016 GOP hopeful Sen. Rand Paul. Speaking to reporters before the event, Paul declined to endorse his colleague Graham, choosing to leave that to the voters of South Carolina. “At this time, I think it’s unlikely that I’ll be involved,” Paul said, “but I haven’t completely closed the door.”

As in the past, Graham’s critics hope someone of significant stature will jump in. “Trey Gowdy could beat him. Mick Mulvaney could beat him,” says a strategist who’s been involved in several Senate races nationwide. He was referring to two popular conservative House members from South Carolina, neither of whom has expressed interest in running.

Still, any big-foot challenger has time to consider the race; the candidate filing deadline is next spring. And the system provides for a runoff if Graham can’t crack 50 percent of the primary vote.

“If he gets into a runoff, Graham will be in deep, deep trouble,” says the strategist.

Given that, it would not be surprising if some conservative group runs ads against Graham in coming months. The idea would not be to promote any other candidate, but to push down Graham’s approval numbers and hopefully entice a big-name candidate into the race.

The bottom line is that the odds favor Graham. But if a few factors line up for his opponents, this might be his toughest race yet.

Byron York is chief political correspondent for The Washington Examiner.